# Sanchez

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I really appreciate it when you take time to answer my questions. Thanks!

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 Feb4 awarded Nice Answer Feb1 comment The zeta-function of Fibonacci sequence? There is a reason to consider zeta function for the sequence "number of points of a variety mod p^n". I'm not sure if the zeta function for a general sequence is of interest. Feb1 comment The zeta-function of Fibonacci sequence? It looks right. Can you give a reference on zeta function on a sequence in general? Jan31 comment Why should the tangent bundle of the boundary of a conctractible manifold be stably trivial? and the normal bundle is trivial, no?(Fix a metric, and take the unit outward vector field) Jan31 comment for any $a$ belongs to $\mathbb{C}$ $f(z_i)=a$ holds for $z_1,z_2,..;z_n$ Show that $\infty$ is not an essential singularity for $f$ using Picard. This will force $f$ to be a polynomial. Degree $n$ comes from your condition. Jan31 comment Open Subgroups of Affine algebraic groups You say it's connected - then $H$ should be the same as $G$, since the union of all other cosets of $H$ form an open set disjoint from $H$. Jan31 answered Inequality. $\frac{x^3}{y^2+z^2}+\frac{y^3}{z^2+x^2}+\frac{z^3}{x^2+y^2} \geq \dfrac{3}{2}.$ Jan31 awarded Organizer Jan31 revised A reference to study p-admissible functions edited tags Jan31 answered Exterior Algebra as quotient Jan30 comment A Dirichlet Convolution involving $\mu(n)$ and $\log n$ $\sum_{d|n} \mu(d)/d = \prod_{p|n} (1-1/p) = \phi(n)/n$ instead of $\phi(n)$. A similar mistake happens in your treatment of the second term - I believe that the final answer shouldn't have the $n$ factor in front. Jan29 comment $a^m+k=b^n$ Finite or infinite solutions? This probably follows from Siegel's theorem directly. Jan29 comment Primes of the form $n^{3} + 2$ It is however known that there are infinitely many primes of the form $x^3+2y^3$ (Heath-Brown). Jan29 comment Defining the Riemann-Roch space of a divisor @porkramen, write down such a linear combination, and let $Gal(\bar{K}/K)$ acts on it. All the $K(E)$ elements are fixed, so you would get a different linear combination unless all the coefficients are in $K$ already. If there is a different linear combination, take the difference with the original combination, we get linear dependence between the basis elements, contradiction. Jan29 comment Formal identity for sum of polynomials over a finite field. I meant to say that $\sigma(fg) = \sigma(f)\sigma(g)$ if $f$,$g$ are relatively prime. This, together with $F[x]$ is UFD, gives that LHS = $\prod_f \sum_{n=o}^{\infty} \sigma (f^n) |f|^{-ns}$. Simplifying this would probably give you what you want, but the answer below is definitely simpler. Jan29 comment Formal identity for sum of polynomials over a finite field. Have you used LHS is multiplicative? Jan29 comment How show that $\lim_{\varepsilon \rightarrow 0}\int_A h_\varepsilon(x)dx =0$, whenever $\bigg|\int_I h\bigg|\leq |I|^{1/2}$? @JacobSchlather, it gives you enough control indeed. First pick $\eta$, this will fix the number of intervals $I_k$ too, then choose a small enough $\epsilon$. Jan29 comment Defining the Riemann-Roch space of a divisor $\bar{K}$-basis, but the basis elements lie in $K(E)$. You can then show that if an element in $K(E)$ is written as linear sum of this basis, then the coefficients all lie in $K$. Jan29 answered Tangent Space Exercise Jan29 comment Finding a bound on $f'$ Fix an upper bound $B$ of $f$ on the unit circle. Use the given condition to get a bound of $f$ on a circle of radius $r$ (something like $Br$). Now use Cauchy's integral formula for $f'(z)$, and try to show that $f'(z)$ is bounded.